Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math

n = int(input())
a = 1
b = 1
c = -(2*n)
d = (b**2) - (4*a*c)
flag = 0
sol = (-b+math.sqrt(d))//(2*a)
ma = int(sol)
temp = 0
for i in range(1,ma+1):
    temp += i
    c = -(2*(n-temp))
    d = (b**2) - (4*a*c)
    sol = (-b + math.sqrt(d)) // (2 * a)
    if (sol*(sol+1))//2 + temp == n and sol > 0:
        flag = 1
        print("YES")
        break
if flag == 0:
    print("NO")